Icardi joined PSG on an initial loan deal ahead of the closure of the transfer window, having become a fringe figure at Inter following the arrival of coach Antonio Conte, who signed Romelu Lukaku and Alexis Sanchez.
The Argentina striker had previously endured frosty relations with the Nerazzurri, too, and his departure always seemed likely.
De Laurentiis confirmed he made a move for Icardi, yet he had no issue with the player opting to join the likes of Neymar, Kylian Mbappe and Edinson Cavani at PSG instead.
"To buy [Icardi], I came to Inter with an offer of €60million, plus bonuses for a total of €65million," he told Corriere dello Sport. "For Wanda Nara, for her husband's contract, I proposed a gross of about €12million.
"Icardi is not stupid and perhaps he understood that to re-launch himself at European level, it was the best choice to go to a team like PSG, where he can stand out more easily than at Napoli."
Napoli instead signed Fernando Llorente following his release from Tottenham.
And De Laurentiis revealed head coach Carlo Ancelotti had made Llorente his preferred option all along.
"Llorente wasn't my idea but rather Ancelotti's," he said. "No-one would have turned their back on a top player like Icardi but, from the first moment, Ancelotti wanted Llorente.
"He argued that, in attack, we were already heavily stocked and only needed a champion to play in the last 30 minutes of games that required unlocking."
Therefore, with Arkadiusz Milik another option, De Laurentiis has no regrets about the failed transfer.
"I never regret in life. The arrival of Icardi would have prevented the purchase of Llorente, of whom I am as convinced as Ancelotti," he said.
"Above all, he would have overshadowed Milik, who I continue to consider the true big star of the Napoli attack."